Find the Exact Value cos(9pi)

Problem

cos(9*π)

Solution

1. Identify the periodicity of the cosine function. The cosine function has a period of 2*π meaning cos(θ)=cos(θ+2*n*π) for any integer n

2. Reduce the angle by subtracting multiples of 2*π to find the coterminal angle within the interval [0,2*π)

θ=9*π−4*(2*π)

θ=9*π−8*π

θ=π

3. Evaluate the cosine of the resulting angle. On the unit circle, the coordinates at π radians are (−1,0) Since cos(θ) corresponds to the xcoordinate:

cos(π)=−1

Final Answer

cos(9*π)=−1

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